Alison Hume, 44, died following delays in her rescue after fire chiefs stopped rank-and-file firefighters from trying to reach the victim, choosing instead to wait for mountain rescue crews to arrive at the shaft in Galston, East Ayrshire.
A Fatal Accident Inquiry (FAI) earlier this month noted that a "preoccupation" with fire brigade policy had left the service "detached" from the situation they were dealing with in July 2008.
Mrs Hume died from a heart attack after being lifted out of the shaft, some six hours after her daughter called 999 to alert emergency services to the accident. She had spent almost eight hours underground.
First Minister Alex Salmond later announced that an inquiry, only the second of its kind in Scotland, would be set up to look at how such incidents are dealt with.
HM chief inspector of fire and rescue authorities Steven Torrie will carry out the investigation, which will look at whether appropriate steps have been taken to minimise the chance of such a tragedy from happening again.
The inquiry will consider whether the policies, procedures and practices now in place in Strathclyde Fire and Rescue adequately address the issues raised in the FAI.
It will consider whether the sheriff's findings have implications for fire and rescue services across Scotland as a whole, including an assessment of whether lessons have been learned from the case.
The inquiry will also consider whether any actions should be recommended to the current eight fire and rescue services in Scotland, and the proposed new single fire service.
When the findings of the FAI were published, Strathclyde Fire and Rescue Service said its members had faced a "uniquely challenging" situation and it was a "source of enormous regret" they had been unable to rescue Mrs Hume.
The service apologised to Mrs Hume's family and defended its approach on the night, claiming the equipment first available on the ground at the time could have put Mrs Hume's life further at risk.
Sheriff Desmond Leslie, who conducted the FAI, described in his report "a preoccupation with adherence to Strathclyde Fire and Rescue Service policy which was entirely detached from the event with which Strathclyde Fire and Rescue Service was confronted."
He said: "There was clearly a balance to be struck between the interests and safety of the rescuers, and those of the casualty they were there to rescue."
The new inquiry is due to report its findings by the end of March next year.